After an interval of three or four centuries from the time of Theodosius, we meet with the names of Pappas, the commentator of Apollo nius, Theon, the commentator of Ptolemy, and of Proclus, another commentator on the ancient mathematicians. The destruction of the li brary of Alexandria by the Saracens was very fatal to the cultivation of geometry, which had flourished there more than any where else : all the geometricians from every part had as sembled there, and when driven away they were deprived both of their books and Instru ments. It is not surprising, therefore, that the study of geometry was for 'many centu ries almost entirely forgotten amidst the troubles which desolated all Europe on the ir ruption of the northern tribes. The Arabs, who by the ravages they committed at Alex andAa, had done the most injury to the science of geometry, were, after the lapse of two cen turies, the cultivators of that which they had nearly annihilated. They studied the works of the Greeks, and showed their proficiency in the correctness oftheir comments on these writings.
Whilst the Arabs were thus promoting the cause of science generally, Europe remained in a state of comparative barbarism, nor was the study of geometry revived among the Europeans before the fourteenth and fifteenth centuries, when by the translations of the ancient writings, the taste for geometry be came very general among the thinking part of the community. In the following century
there arose mathematicians who added very materially to the stock of geometrical know ledge. Carden applied algebra to the resolu tion of geometrical problems; and Descartes, who followed at the distance of nearly a cen tury, pursued this application of algebra to geometry still farther. At the same period with Descartes flourished Cavelerius, who, in his work on 'Indivisibles,' struck out a new path to himself, in which he was followed by many writers of great celebrity, as Wallis, Pascal, Fermat, Roberval, Liebnitz, Newton, and many others, who set forth geometry in a new light, and formed a new system of the science. Among the treatises in which are embodied the geometrical principles of the moderns and ancients may be reckoned the Elements of Euclid by Simson and Playfair, the treatises of Ozanam, Clavius, Bonny castle, Hutton, RT.e.